EVALUATING THE PERFORMANCE OF ORDINARY LEAST SQUARE AND POLYNOMIAL REGRESSION WITH RESPECT TO SAMPLE SIZE
Keywords:
ordinary least square OLS polynomial regression PR, Root mean square error (RMSE), Mean square error (MSE)Abstract
The evaluation of Ordinary Least Squares (OLS) and polynomial regression (PR) on their predictive performance was studied. We used simulated data to evaluate the performance of estimators using small and large sample. However, the mean square error (MSE (????̂ 0 ); MSE(????̂ 1) and MSE(????̂)) ware used to find out the most efficient among the estimated models. The results show that, for ???? = 1000 the OLS is efficient than the PR due to having the least MSE (????̂ 0 ); MSE(????̂ 1) and MSE(????̂) on both normal and log-normal distributions. Whereas for ???? = 3000 the values of MSE (????̂ 0 ); MSE(????̂ 1) and MSE(????̂) of PR are little bit lower than that of OLS which indicates the efficiency of PR over OLS on both distributions. Finally, For, ???? = 5000 the values of MSE (????̂ 0 ); MSE(????̂ 1) and MSE(????̂) of PR are much more lower than that of OLS which shows that PR is efficient than OLS on both distributions. Overall, the results suggest that OLS is more efficient than PR for smaller sample sizes and PR is more efficient for bigger sample sizes.
